Effective results for linear equations in members of two recurrence sequences

Let $(U_n)_{n=0}^\infty$ and $(V_m)_{m=0}^\infty$ be two linear recurrence sequences. For fixed positive integers $k$ and $\ell$, a fixed $k$-tuple $(a_1,\dots,a_k)\in \mathbb{Z}^k$ and a fixed $\ell$-tuple $(b_1,\dots,b_\ell)\in \mathbb{Z}^\ell$ we consi